Equivalence of K-Functionals and Modulus of Smoothness Constructed by the Mehler-Fock-Clifford Transform

El Bouazizi, Mohammed; El Hamma, Mohamed

doi:10.28919/cpr-pajm/5-6

Research article

Equivalence of K-Functionals and Modulus of Smoothness Constructed by the Mehler-Fock-Clifford Transform

Mohammed El Bouazizi, Mohamed El Hamma

Abstract

Using the Mehelt-Fock-Clifford transform, we define generalized modulus of smoothness in the space \(L^2(J;x^{-\frac{1}{2}}dx)\). Based on the kernel \(P_{i\sqrt{\lambda}-\frac{1}{2}}\) and the operator \(A_x^m\) we define Sobolev-type and \(K\)-functionals. The main result of the paper is the proof of the equivalence theorem for a \(K\)-functional and a modulus of smoothness for the Mehler-Fock-Clifford transform.

How to cite

M. El Bouazizi, M. El Hamma, Equivalence of K-Functionals and Modulus of Smoothness Constructed by the Mehler-Fock-Clifford Transform, Pan-Amer. J. Math. 5 (2026), 6. https://doi.org/10.28919/cpr-pajm/5-6

BibTeX

@article{Bouazizi2026,
  author  = {El Bouazizi, Mohammed and El Hamma, Mohamed},
  title   = {Equivalence of K-Functionals and Modulus of Smoothness Constructed by the Mehler-Fock-Clifford Transform},
  journal = {Pan-Amer. J. Math.},
  volume  = {5},
  year    = {2026},
  pages   = {6},
  doi     = {10.28919/cpr-pajm/5-6}
}